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Journal ArticleDOI

Universal upper bound on the entropy-to-energy ratio for bounded systems

15 Jan 1981-Physical Review D (American Physical Society)-Vol. 23, Iss: 2, pp 287-298
TL;DR: For systems with negligible self-gravity, the bound follows from application of the second law of thermodynamics to a gedanken experiment involving a black hole as discussed by the authors, and it is shown that black holes have the maximum entropy for given mass and size which is allowed by quantum theory and general relativity.
Abstract: We present evidence for the existence of a universal upper bound of magnitude $\frac{2\ensuremath{\pi}R}{\ensuremath{\hbar}c}$ to the entropy-to-energy ratio $\frac{S}{E}$ of an arbitrary system of effective radius $R$. For systems with negligible self-gravity, the bound follows from application of the second law of thermodynamics to a gedanken experiment involving a black hole. Direct statistical arguments are also discussed. A microcanonical approach of Gibbons illustrates for simple systems (gravitating and not) the reason behind the bound, and the connection of $R$ with the longest dimension of the system. A more general approach establishes the bound for a relativistic field system contained in a cavity of arbitrary shape, or in a closed universe. Black holes also comply with the bound; in fact they actually attain it. Thus, as long suspected, black holes have the maximum entropy for given mass and size which is allowed by quantum theory and general relativity.
Citations
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Journal ArticleDOI
TL;DR: In this paper, it is argued that underlying the Church-Turing hypothesis there is an implicit physical assertion: every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means.
Abstract: It is argued that underlying the Church-Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means’. Classical physics and the universal Turing machine, because the former is continuous and the latter discrete, do not obey the principle, at least in the strong form above. A class of model computing machines that is the quantum generalization of the class of Turing machines is described, and it is shown that quantum theory and the ‘universal quantum computer’ are compatible with the principle. Computing machines resembling the universal quantum computer could, in principle, be built and would have many remarkable properties not reproducible by any Turing machine. These do not include the computation of non-recursive functions, but they do include ‘quantum parallelism’, a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it. The intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than Everett’s. Some of the numerous connections between the quantum theory of computation and the rest of physics are explored. Quantum complexity theory allows a physically more reasonable definition of the ‘complexity’ or ‘knowledge’ in a physical system than does classical complexity theory.

3,670 citations

Journal ArticleDOI
TL;DR: It is provided evidence that this value of shear viscosity to volume density of entropy may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.
Abstract: The ratio of shear viscosity to volume density of entropy can be used to characterize how close a given fluid is to being perfect. Using string theory methods, we show that this ratio is equal to a universal value of [h-bar]/4pikB for a large class of strongly interacting quantum field theories whose dual description involves black holes in anti–de Sitter space. We provide evidence that this value may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.

2,721 citations

Journal ArticleDOI
19 Nov 2004-Science
TL;DR: This work has shown that conventional bounds to the precision of measurements such as the shot noise limit or the standard quantum limit are not as fundamental as the Heisenberg limits and can be beaten using quantum strategies that employ “quantum tricks” such as squeezing and entanglement.
Abstract: Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurement. Conventional measurement techniques typically fail to reach these limits. Conventional bounds to the precision of measurements such as the shot noise limit or the standard quantum limit are not as fundamental as the Heisenberg limits and can be beaten using quantum strategies that employ “quantum tricks” such as squeezing and entanglement.

2,421 citations

Book
01 Jan 2001
TL;DR: Conservative logic shows that it is ideally possible to build sequential circuits with zero internal power dissipation and proves that universal computing capabilities are compatible with the reversibility and conservation constraints.
Abstract: Conservative logic is a comprehensive model of computation which explicitly reflects a number of fundamental principles of physics, such as the reversibility of the dynamical laws and the conservation of certain additive quantities (among which energy plays a distinguished role). Because it more closely mirrors physics than traditional models of computation, conservative logic is in a better position to provide indications concerning the realization of high-performance computing systems, i.e., of systems that make very efficient use of the "computing resources" actually offered by nature. In particular, conservative logic shows that it is ideally possible to build sequential circuits with zero internal power dissipation. After establishing a general framework, we discuss two specific models of computation. The first uses binary variables and is the conservative-logic counterpart of switching theory; this model proves that universal computing capabilities are compatible with the reversibility and conservation constraints. The second model, which is a refinement of the first, constitutes a substantial breakthrough in establishing a correspondence between computation and physics. In fact, this model is based on elastic collisions of identical "balls" and thus is formally identical with the atomic model that underlies the (classical) kinetic theory of perfect gases. Quite literally, the functional behavior of a general-purpose digital computer can be reproduced by a perfect gas placed in a suitably shaped container and given appropriate initial conditions.

1,888 citations

Journal ArticleDOI
TL;DR: The holographic principle as mentioned in this paper asserts that the fundamental degrees of freedom involved in a unified description of spacetime and matter must be manifest in an underlying quantum theory of gravity, and it has yet to be explained.
Abstract: There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at $1.4\ifmmode\times\else\texttimes\fi{}{10}^{69}$ bits per square meter. This article reviews the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. This article explains how the bound is tested, and its validity is demonstrated in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. This article surveys some successes and challenges in implementing the holographic principle.

1,706 citations


Cites background from "Universal upper bound on the entrop..."

  • ...The entropy bounds discussed in this section are “universal” (Bekenstein, 1981) in the sense that they are independent of the specific characteristics and composition of matter systems....

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  • ...oblem, as one may define R in terms of the surface area. A Schwarzschild black hole in four dimensions has R = 2E. Hence, its Bekenstein entropy, S = A/4 = πR2, exactly saturates the Bekenstein bound (Bekenstein, 1981). In D > 4, black holes come to within a factor 2 D−2 of saturating the bound (Bousso, 2001). 10 C. Spherical entropy bound Instead of dropping a thermodynamic system into an existing black hole vi...

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  • ...(2.9), has much empirical support (Bekenstein, 1981, 1984; Schiffer and Bekenstein, 1989)....

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  • ...Hence, its Bekenstein entropy, S = A/4 = πR2, exactly saturates the Bekenstein bound (Bekenstein, 1981)....

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  • ... one would not expect quantum buoyancy to play a crucial role. 3. Empirical status Independently of its logical relation to the GSL, one can ask whether the Bekenstein bound actually holds in nature. Bekenstein (1981, 1984) and Schiffer and Bekenstein (1989) have made a strong case that all physically reasonable, weakly gravitating matter systems satisfy Eq. (2.9); some come within an order of magnitude of saturat...

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